You are looking for the BBB or BBW; that's Broad Breasted Bronze or WHite; the white will grow a bit bigger than the bronze and is the one seen 99.9% of the grocery store birds. Hatch to market in 4 months. SUper fast growth, and a much bigger amount of breast meat. Great feed conversion. By feeding it yourself, it will taste way better than the grocery store bird.
The heritage birds are a slower growing bird and mature at usually a smaller size and with a smaller breast size. This bird can forage for some of its feed a little better than the BBW/BBB. THis bird can be bred by the back yard poultry owner. The BBW/BBB is a specially bred bird; with the extremely large breast, it needs the skills of a technician to use AI for breeding.
Hope this helps.